Periodic Orbits and Homoclinic Orbits of Second-order Hamiltonian Systems with Mild Superquadratic Growth
Xiaofei Zhang , Chungen Liu , Benxing Zhou
Frontiers of Mathematics ›› 2025, Vol. 20 ›› Issue (4) : 855 -871.
Periodic Orbits and Homoclinic Orbits of Second-order Hamiltonian Systems with Mild Superquadratic Growth
Using the saddle point theorem and the mountain pass theorem with Morse index estimate, the existence of periodic solutions for second-order Hamiltonian systems with mild superquadratic growth is proved in this paper. Meanwhile the existence result of homoclinic orbits for this kind of Hamiltonian systems is also obtained by the local convergence of a sequence of subharmonic solutions.
Hamiltonian system / periodic solution / homoclinic orbit / Morse index
Peking University
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